NZMATH  1.2.0
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nzmath.intresidue.IntegerResidueClassRing Class Reference
Inheritance diagram for nzmath.intresidue.IntegerResidueClassRing:
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Collaboration diagram for nzmath.intresidue.IntegerResidueClassRing:
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Public Member Functions

def __init__ (self, modulus)
 
def __repr__ (self)
 
def __str__ (self)
 
def __hash__ (self)
 
def card (self)
 
def getInstance (cls, modulus)
 
def createElement (self, seed)
 
def getCharacteristic (self)
 
def __contains__ (self, elem)
 
def isfield (self)
 
def __eq__ (self, other)
 
def __ne__ (self, other)
 
def issubring (self, other)
 
def issuperring (self, other)
 
- Public Member Functions inherited from nzmath.ring.CommutativeRing
def __init__ (self)
 
def getQuotientField (self)
 
def isdomain (self)
 
def isnoetherian (self)
 
def isufd (self)
 
def ispid (self)
 
def iseuclidean (self)
 
def registerModuleAction (self, action_ring, action)
 
def hasaction (self, action_ring)
 
def getaction (self, action_ring)
 
- Public Member Functions inherited from nzmath.ring.Ring
def getCommonSuperring (self, other)
 

Public Attributes

 m
 
- Public Attributes inherited from nzmath.ring.CommutativeRing
 properties
 

Static Public Attributes

def isdomain = isfield
 
def isnoetherian = isfield
 
def isufd = isfield
 
def ispid = isfield
 
def iseuclidean = isfield
 

Properties

 one = property(_getOne, None, None, "multiplicative unit.")
 
 zero = property(_getZero, None, None, "additive unit.")
 

Private Member Functions

def _getOne (self)
 
def _getZero (self)
 

Private Attributes

 _one
 
 _zero
 

Static Private Attributes

dictionary _instances = {}
 

Detailed Description

IntegerResidueClassRing is also known as Z/mZ.

Definition at line 218 of file intresidue.py.

Constructor & Destructor Documentation

◆ __init__()

def nzmath.intresidue.IntegerResidueClassRing.__init__ (   self,
  modulus 
)
The argument modulus m specifies an ideal mZ.

Definition at line 225 of file intresidue.py.

Member Function Documentation

◆ __contains__()

def nzmath.intresidue.IntegerResidueClassRing.__contains__ (   self,
  elem 
)

◆ __eq__()

◆ __hash__()

def nzmath.intresidue.IntegerResidueClassRing.__hash__ (   self)

◆ __ne__()

def nzmath.intresidue.IntegerResidueClassRing.__ne__ (   self,
  other 
)
Inequality test.

Reimplemented from nzmath.ring.Ring.

Definition at line 307 of file intresidue.py.

◆ __repr__()

def nzmath.intresidue.IntegerResidueClassRing.__repr__ (   self)

◆ __str__()

def nzmath.intresidue.IntegerResidueClassRing.__str__ (   self)

◆ _getOne()

◆ _getZero()

◆ card()

def nzmath.intresidue.IntegerResidueClassRing.card (   self)
Return the cardinality of the ring.

Definition at line 245 of file intresidue.py.

References nzmath.intresidue.IntegerResidueClass.m, and nzmath.intresidue.IntegerResidueClassRing.m.

◆ createElement()

def nzmath.intresidue.IntegerResidueClassRing.createElement (   self,
  seed 
)
createElement returns an element of the ring with seed.

Reimplemented from nzmath.ring.Ring.

Definition at line 263 of file intresidue.py.

References nzmath.intresidue.IntegerResidueClass.m, and nzmath.intresidue.IntegerResidueClassRing.m.

Referenced by nzmath.finitefield.FiniteField.random_element(), and nzmath.finitefield.FiniteField.TonelliShanks().

◆ getCharacteristic()

def nzmath.intresidue.IntegerResidueClassRing.getCharacteristic (   self)
The characteristic of Z/mZ is m.

Reimplemented from nzmath.ring.Ring.

Definition at line 271 of file intresidue.py.

References nzmath.intresidue.IntegerResidueClass.m, and nzmath.intresidue.IntegerResidueClassRing.m.

◆ getInstance()

def nzmath.intresidue.IntegerResidueClassRing.getInstance (   cls,
  modulus 
)
getInstance returns an instance of the class of specified
modulus.

Definition at line 252 of file intresidue.py.

References nzmath.finitefield.FinitePrimeField._instances, and nzmath.intresidue.IntegerResidueClassRing._instances.

◆ isfield()

def nzmath.intresidue.IntegerResidueClassRing.isfield (   self)
isfield returns True if the modulus is prime, False if not.
Since a finite domain is a field, other ring property tests
are merely aliases of isfield.

Reimplemented from nzmath.ring.CommutativeRing.

Definition at line 283 of file intresidue.py.

References nzmath.intresidue.IntegerResidueClass.m, nzmath.intresidue.IntegerResidueClassRing.m, and nzmath.ring.CommutativeRing.properties.

◆ issubring()

def nzmath.intresidue.IntegerResidueClassRing.issubring (   self,
  other 
)
Report whether another ring contains the ring as a subring.

Reimplemented from nzmath.ring.Ring.

Definition at line 310 of file intresidue.py.

Referenced by nzmath.ring.Ring.getCommonSuperring(), nzmath.rational.RationalField.getCommonSuperring(), and nzmath.rational.IntegerRing.getCommonSuperring().

◆ issuperring()

Member Data Documentation

◆ _instances

◆ _one

◆ _zero

◆ isdomain

def nzmath.intresidue.IntegerResidueClassRing.isdomain = isfield
static

Definition at line 296 of file intresidue.py.

◆ iseuclidean

def nzmath.intresidue.IntegerResidueClassRing.iseuclidean = isfield
static

Definition at line 300 of file intresidue.py.

◆ isnoetherian

def nzmath.intresidue.IntegerResidueClassRing.isnoetherian = isfield
static

Definition at line 297 of file intresidue.py.

◆ ispid

def nzmath.intresidue.IntegerResidueClassRing.ispid = isfield
static

Definition at line 299 of file intresidue.py.

◆ isufd

def nzmath.intresidue.IntegerResidueClassRing.isufd = isfield
static

Definition at line 298 of file intresidue.py.

◆ m

Property Documentation

◆ one

◆ zero

nzmath.intresidue.IntegerResidueClassRing.zero = property(_getZero, None, None, "additive unit.")
static

Definition at line 336 of file intresidue.py.

Referenced by nzmath.ring.Field.gcd(), and nzmath.matrix.MatrixRing.zeroMatrix().


The documentation for this class was generated from the following file: